Jan 23, 2017: Stellar Day
We made so many theorems today. It is wonderful.
Mr Barker gave an argument for Conjecture B. The argument required the use of Theorem 1.7, so we must add the assumption that the diagonals of the rhombus cross.
Mr Peters gave an argument for 1.2 using a proof by contradiction. Since it involves what is essentially an impossible figure, it was challenging to follow. But in the end the contradiction happens by finding a triangle which has angles which are too big.
Ms Lewis gave another argument for 1.2. Her method is direct and relies on Postulate 5.
Mr Schmidt gave a proof that the second statement of Conjecture 1.1 is false. Essentially, he proves that the example rhombus constructed in Ms Lewis’ solution to 1.4 fails to have the property required.
We talked briefly about how many bits of our work put together gives a (positive) solution to Conjecture C.
Tasks Update
Our current list of open problems is: 1.3, 1.5
That’s too short, so I have posted the next section of the task sequence. This is about the idea of a kite. This is a generalization of the notion of rhombus.
Department of Mathematics 0506
University of Nothern Iowa
Cedar Falls, IA 50613-0506
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Phone: 319-273-2646
email: theron.hitchman@uni.edu
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